1. Field of the Invention
The invention relates to spatial light modulators, and more specifically to spatial light modulators wherein full complex modulation is achieved by superimposing the output of more than one modulator.
2. Description of the Related Art
Spatial light modulators (SLMs) are devices used to control the distribution of light in an optical system. Such devices have many uses including signal processing and pattern recognition.
Generally, the light modulation characteristics of most SLMs are coupled combinations of amplitude and phase changes. The modulation characteristic of a picture element (pixel) is controlled by a single applied signal, (electrical voltage, current, or incident optical intensity level, for example) and, because they are coupled, phase change and amplitude cannot be independently controlled.
U.S. Pat. No. 5,148,157 to Florence, incorporated herein and made a part hereof, teaches a method of controlling the amplitude and phase modulation of light independently and simultaneously by dividing the pixels into more than one modulating element per pixel, independently controlling the sub-elements, and subsequently combining the partial modulation results by optically under-resolving them into pixels.
Optimizing of the signal to noise ratio, as well as other operations using lightwaves, is enhanced by using spatial light modulators (SLMs) that can express full complex behavior. Typically, the action of an SLM is restricted to certain locations in the complex plane characteristic of the particular SLM, called its operating curve.
As noted above, in the art of optical information processing it is frequently desirable to have light modulation that can take an arbitrary complex value. Consideration must be given to physical limitations; for example, a purely passive light modulator might have any phase between 0 and 2.pi. radians, but its amplitude is necessarily less than unity. The values of the modulator's action might be specified in terms of their real and imaginary parts, or equivalently, in terms of their amplitude and phase. As is often customary in optical information processing, the action herein is described in terms of amplitude and phase. In order to produce arbitrary values of modulation it is necessary to have independent control of amplitude and phase. To effect fully complex modulation in an optical processing system one might resort to such methods as volume holography. However, the volume holographic method is not optimal for a real-time optical information processing system, since this method is ordinarily based on photographic emulsion that is not rapidly programmable. See for example, virtually any of the articles, and their references, in Optical Pattern Recoqnition: proceedings of a conference held 4 Nov. 1991, San Jose Calif./sponsored by SPIE--the International Society for Optical Engineering; Joseph L. Horner, Bahram Javidi, editors. Methods of optimizing optical information processing under the limitations imposed by existing rapidly programmable spatial light modulators are well known.
Reference herein is routinely made to pixels, or picture elements, since many of the spatial light modulators on which the invention could be implemented are controlled at a discrete set of locations. It will be understood by those familiar with the art that the description applies as well to those spatial light modulators that are controlled from a continuum of locations, as for example in a light-addressed light valve.
Ordinarily the rapidly reconfigurable spatial light modulators one can conveniently install in optical correlators respond to a single drive parameter and so cannot achieve fully independent amplitudes and phases. Illustrative examples are: the optically addressed and continuously variable liquid crystal light valves manufactured by Hughes, the electrically addressed and continuously variable deformable mirror device manufactured by Texas Instruments, and the electrically addressed and binary magneto-optic device manufactured by Litton. The point is that a single modulator, responding to a single drive parameter, cannot produce an arbitrary complex value of modulation. Signal processing theory shows that access to a fully complex set of filter values is better than access to only a limited set. The classical matched filter, for example, produces the highest signal to noise ratio under some standard circumstances. Yet the existing rapidly changeable and continuously variable modulators have access to at best a one-parameter curve in the complex plane. Discretely variable modulators are even further limited. Consequently, a good deal of effort has gone into finding the optimum representation of a desired filter, given that the filter must be expressed on the operating curve of the continuously variable light modulator. The performance of a correlator would be improved were each pixel in the filter modulator to be fully complex. An additional benefit of the invention relates to optically encoding a signal for later processing. The action of a continuously variable modulator generally couples its effect between amplitude and phase. Thus an optically encoded drive signal would have both phase and amplitude in its physical expression, a circumstance that has some deleterious effects. For a specific example, any phase coupling into the encoding process causes a loss of scale invariance and linearity in the encoded signal. If the signal is encoded at constant phase and variable amplitude, the transform of the encoded signal is scale invariant. That is, when the input signal to be encoded (typically a real scalar) undergoes multiplication by a constant factor, the Fourier transform of the encoded signal then undergoes multiplication by the same constant factor. However, if phase varies with the drive applied to the spatial light modulator, the encoded signal (and also its transform) do not have scale invariance. The effect is well known and is analyzed in terms of the spectral content of frequency modulation (FM) signals.
It is, therefore, an object of the invention to allow constant-phase encoding of signals even with modulators that may have phase variation in their action, with the consequent benefits of scale invariance to optical processing of the encoded signal.
Clearly, to reach an arbitrary point within a region of the complex plane, two independent coordinates are to be controlled. In the present invention, the actions of two independent pixels are averaged together placing their virtual locations into optical conjunction.
U.S. Pat. No. 5,148,157 to Florence teaches a different method of achieving fully complex modulation. Dr. Florence's invention relies on direct adjacency of the addressed pixels, with the averaging action occurring by way of optically under-resolving a pair of pixels.
It is a further object of the present invention, therefore, to take full advantage of the space-bandwidth product (here, taken as the pixel count) of each modulator. Thus, the present invention can be implemented at full pixel count using conventional existing modulators, without resorting to special shaping of addressed pixels or changing the geometry of addressing leads.
It is an additional object of the invention to allow the use of multiple adjacent diffraction orders of the composite modulator's far-field pattern, whereas the Florence invention necessitates blocking the high-frequency components by optically under-resolving the single-plane pixels. It is a still further object of the invention to realize a convenience, when mathematically decomposing a desired fully complex action into separate parts which are to be exercised on the two component spatial light modulators, that one need not take into account a spatial translation between the elements that represent the action. This is a simple and direct result of the independence of the participating pixels. They are placed into optical conjunction with each other, so that there is no translation to take into account.
It is a still further additional object of the invention to realize the optical joint transform of two patterns, one written onto each of the two component modulators. In conventional optical joint transform correlation, the patterns are written onto modulators that are placed side-by-side in the input plane of the correlator. This side-by-side positioning results in a spatial shift of the two patterns input to the joint transform correlator, and even when such spatial shift is a minimum, it translates to a minimum spatial frequency in the transform plane. It is occasionally inconvenient to deal with this frequency shift, even when it is a minimum. The present invention is easily seen to permit a smaller between-pattern translation dimension; indeed, zero relative translation (corresponding to direct superposition of the patterns) may be realized.
It is yet another object of the invention to produce an overall shift in the operating curve of a single addressable spatial light modulator by combining its operation with a static offset from a simple unaddressed surface.